.bowerrc

{
  "directory": "vendor/bower_components"
}

bower.json

{
  "name": "Bootstrap powered Application",
  "dependencies": {
    "bootstrap-sass-official": "~3.3.4"
  }
}

gulpfile.js

var elixir = require('laravel-elixir');
elixir.config.sourcemaps = false;

var paths = {
    'jquery': './vendor/bower_components/jquery/',
    'bootstrap': './vendor/bower_components/bootstrap-sass-official/assets/'
}

elixir(function(mix) {
    mix.sass('app.scss', 'public/css/', {includePaths: [paths.bootstrap + 'stylesheets/']})
       .copy(paths.bootstrap + 'fonts/bootstrap/**', 'public/fonts')
       .scripts([
            paths.jquery + 'dist/jquery.min.js',
            paths.bootstrap + 'javascripts/bootstrap.min.js'
        ], 'public/js/app.js', './');
});